addition

Effective MathReps for Addition with Regrouping

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Today, we’re diving into second-grade math with a MathRep that focuses on addition with regrouping.

In our previous posts, we explored using MathReps for addition and subtraction without regrouping. Now, we’re taking it a step further and tackling regrouping, helping students make the jump from pictorial models to expanded notation and the base 10 system.

So, buckle in—let’s get started!

Step-by-Step Guide: Regrouping with MathReps

Set Up the Numbers

For this example, we’re adding 682 + 234, and we’ll use a pictorial model to visually represent the numbers before transitioning into the expanded form.

Solve Using a Pictorial Model

1️⃣ Start with the Ones Place:

  • 2 + 4 = 6
  • No regrouping needed here, so we write 6 in the ones place.

2️⃣ Move to the Tens Place:

  • We add 8 tens + 3 tens = 11 tens, which equals 110.
  • Since 10 tens = 100, we regroup by circling ten tens and moving them into the hundreds place.
  • This leaves 1 ten (10) in the tens place.

3️⃣ Move to the Hundreds Place:

  • We now have 6 hundreds + 2 hundreds + 1 regrouped hundred = 9 hundreds.

Bringing it all together:
916

Transition to the Base 10 Model (Expanded Notation)

Now, let’s break it down using expanded form:

  • 682 → 600 + 80 + 2
  • 234 → 200 + 30 + 4

Adding the place values:

  • Ones: 2 + 4 = 6
  • Tens: 80 + 30 = 110 → Regroup into 100 + 10
  • Hundreds: 600 + 200 + 100 = 900

Total: 916

Alternative Thinking: Flexible Number Sense

Instead of regrouping immediately, students can leave the tens as 110 and think of the sum as:

800 + 110 + 6 = 916

This approach challenges students to see numbers flexibly before applying the standard algorithm, deepening their conceptual understanding.

Why This Works

MathReps provide a structured, visual approach that helps students bridge the gap between pictorial models and formal mathematical notation. By working through regrouping in different ways, students develop number flexibility and problem-solving confidence.

Get Your Free MathReps!

Want to try this in your classroom? Download your free MathRep template at MathReps.com and explore even more math resources.

💡 Bonus Resource: Check out Wipebook for workbooks featuring MathReps—each workbook includes four MathReps to last the entire year!

Watch the Tutorial Video

Shop ‘Til You Drop

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Recently I have begun to incorporate projects more and more into my classroom. The latest was ‘Shop ‘Til You Drop’. This activity gave students real-world experience adding and subtracting decimals (This is a 5th grade Common Core Standard – NBT.7). It also incorporates 4 other Common Core Standards. It was a project that my partner teacher found online. And like any good teacher, I have had time to reflect on the project; take note of what went well, and what I will do differently next time.

Schöne Geschenke
Photo by geschenkhamster.de via wiki commons
 

 

What went well:

  • Students begged to work on the project.
  • Students took the assignment seriously.
  • Students asked for help with subtracting across zeros – I need to go back and reteach.
  • Students helped one another solve problems and find gifts.
  • Many quality presentations were made.
  • Many students viewed their project on the TV, seeking feedback.
  • Students took feedback and made adjustments – even after their presentation was given.
  • Templates were used and modified.

Things that need improving:

  • Work space on paper (just to make sure they’re not using a calculator).
  • Rubric/Scale that fits my needs – Marzano based.
  • Give more time. Took longer than I anticipated.
  • Ask what student would do with left over money. While some volunteered this information, many did not. It wasn’t something that I thought about until one student shared her thoughts – she wanted to donate the rest to a charity.

And because I am a firm believer in sharing, here is the lesson – templates included. I have included the NETS-S as well. Feel free to share, modify, and use.